Some Refinements of Hermite–Hadamard Type Integral Inequalities Involving Refined Convex Function of the Raina Type

Abstract

The aim of this work is to elaborate and define the idea of refined convex function of the Raina type. In addition, we have attained some associated properties in the manner of the newly introduced idea. To add some more comprehension into the newly investigated definition, we obtain the estimations of the Hermite-Hadamard inequality. For the reader’s interest, we add some remarks regarding the Mittag-Leffer function. During the last four decades, the term Mitag-Leffler function has acquired popularity on account of its many importance in the fields of engineering and science, i.e statistical distribution theory, rheology, electric networks, fluid flow, and probability. The amazing perception regarding this function provides the solution of certain boundary value problems. The asymptotic status of this function plays a very vital performance in various problems of physics associated with fractional calculus. The methodology and amazing tools of this work may serve as an impetus for further research activities in this direction as well.